ABSTRACT
These paradoxes fall into four groups: paradoxes of the infinitely small; paradoxes of the infinitely big; paradoxes of the one and the many; and paradoxes of thought about the infinite. The first two groups reflect an important distinction within the mathematically infinite between what Aristotle called the infinite by division and the infinite by addition:2 a straight line, for example, is infinite by division if between any two points on it there is a third (so there is no limit to how small a segment of the line you can take); it is infinite by addition if beyond any two points on it there is a third (so there is no limit to how large a segment of the line you can take).
